As explained in Kickstart's PHAR architecture, Kickstart will use PHP's phar extension to run when this extension is installed and enabled on your server. However, this has a few drawbacks. The major drawback is that each file in the Kickstart application gets a wrapper path similar to phar://kickstart.php/src/includes/preamble.php. This kind of path may run afoul of PHP's open_basedir restrictions if they are set on your server. The only way to address it is by using Kickstart's built-in PHAR archive extraction feature which bypasses the PHAR extension. This works because the application files are loaded from a path under your site's root which has to be allowed by open_basedir restrictions; if it wasn't allowed, you could not run anything on your server!
First, create a directory called kicktemp in the same directory you have placed Kickstart's .php file. This directory must be writable by Kickstart. Note that this is the same directory you need to create if you are using Kickstart's FTP, SFTP, or Hybrid file extraction mode. If you have trouble running Kickstart, you should try creating this directory and give it 0777 permissions before doing anything other kind of troubleshooting.
Then, create a file named nophar.txt inside that directory. The file can be empty, or have whatever contents you want; it's irrelevant. The mere presence of this file inside the kicktemp directory tells Kickstart to not use PHP's phar extension.